# Speaking Numbers to LLMs: Multi-Wavelet Number Embeddings for Time Series Forecasting

arXiv: https://arxiv.org/abs/2606.26487 · HTML: https://mlsanity.com/paper/2606.26487/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 35 of its 43 references that are in the map.
- First posted on arXiv 25 Jun 2026.

## Builds on (most cited first, 30 of 35)

- [Informer: Beyond Efficient Transformer for Long Sequence Time-Series Forecasting](https://mlsanity.com/paper/2012.07436/) (2020)
- [A Time Series is Worth 64 Words: Long-term Forecasting with Transformers](https://mlsanity.com/paper/2211.14730/) (2022)
- [Autoformer: Decomposition Transformers with Auto-Correlation for Long-Term Series Forecasting](https://mlsanity.com/paper/2106.13008/) (2021)
- [Are Transformers Effective for Time Series Forecasting?](https://mlsanity.com/paper/2205.13504/) (2022)
- [TimesNet: Temporal 2D-Variation Modeling for General Time Series Analysis](https://mlsanity.com/paper/2210.02186/) (2022)
- [Chronos: Learning the Language of Time Series](https://mlsanity.com/paper/2403.07815/) (2024)
- [N-BEATS: Neural basis expansion analysis for interpretable time series forecasting](https://mlsanity.com/paper/1905.10437/) (2019)
- [Time-LLM: Time Series Forecasting by Reprogramming Large Language Models](https://mlsanity.com/paper/2310.01728/) (2023)
- [A decoder-only foundation model for time-series forecasting](https://mlsanity.com/paper/2310.10688/) (2023)
- [Unified Training of Universal Time Series Forecasting Transformers](https://mlsanity.com/paper/2402.02592/) (2024)
- [Large Language Models Are Zero-Shot Time Series Forecasters](https://mlsanity.com/paper/2310.07820/) (2023)
- [MOMENT: A Family of Open Time-series Foundation Models](https://mlsanity.com/paper/2402.03885/) (2024)
- [Non-stationary Transformers: Exploring the Stationarity in Time Series Forecasting](https://mlsanity.com/paper/2205.14415/) (2022)
- [Spectral Temporal Graph Neural Network for Multivariate Time-series Forecasting](https://mlsanity.com/paper/2103.07719/) (2021)
- [TEMPO: Prompt-based Generative Pre-trained Transformer for Time Series Forecasting](https://mlsanity.com/paper/2310.04948/) (2023)
- [ChatTime: A Unified Multimodal Time Series Foundation Model Bridging Numerical and Textual Data](https://mlsanity.com/paper/2412.11376/) (2024)
- [From News to Forecast: Integrating Event Analysis in LLM-Based Time Series Forecasting with Reflection](https://mlsanity.com/paper/2409.17515/) (2024)
- [Language Models Still Struggle to Zero-shot Reason about Time Series](https://mlsanity.com/paper/2404.11757/) (2024)
- [Can LLMs Understand Time Series Anomalies?](https://mlsanity.com/paper/2410.05440/) (2024)
- [TOTEM: TOkenized Time Series EMbeddings for General Time Series Analysis](https://mlsanity.com/paper/2402.16412/) (2024)
- [Context-Alignment: Activating and Enhancing LLM Capabilities in Time Series](https://mlsanity.com/paper/2501.03747/) (2025)
- [Spectral Temporal Graph Neural Network for Trajectory Prediction](https://mlsanity.com/paper/2106.02930/) (2021)
- [TimeDiT: General-purpose Diffusion Transformers for Time Series Foundation Model](https://mlsanity.com/paper/2409.02322/) (2024)
- [TS-Reasoner: Domain-Oriented Time Series Inference Agents for Reasoning and Automated Analysis](https://mlsanity.com/paper/2410.04047/) (2024)
- [FoNE: Precise Single-Token Number Embeddings via Fourier Features](https://mlsanity.com/paper/2502.09741/) (2025)
- [Counterfactual Neural Temporal Point Process for Estimating Causal Influence of Misinformation on Social Media](https://mlsanity.com/paper/2210.07518/) (2022)
- [Estimating Treatment Effects from Irregular Time Series Observations with Hidden Confounders](https://mlsanity.com/paper/2303.02320/) (2023)
- [TemporalBench: A Benchmark for Evaluating LLM-Based Agents on Contextual and Event-Informed Time Series Tasks](https://mlsanity.com/paper/2602.13272/) (2026)
- [When LLM Meets Time Series: Can LLMs Perform Multi-Step Time Series Reasoning and Inference](https://mlsanity.com/paper/2509.01822/) (2025)
- [Fourier Head: Helping Large Language Models Learn Complex Probability Distributions](https://mlsanity.com/paper/2410.22269/) (2024)

## Abstract (arXiv)

Large language models (LLMs) are attractive for context-aware time series forecasting because they can integrate heterogeneous textual signals, yet their discrete, language-oriented tokenization and embedding interfaces are misaligned with continuous numerical values, often harming numerical ordering and forecasting reliability. We propose TempoWave, a plug-and-play temporal wavelet digit interface that maps each scalar observation into digit-wise embeddings constructed from multi-wavelet, multi-scale coefficients. By directly overriding standard token representations, TempoWave seamlessly exposes both fine-grained local fluctuations and macro global structures in a transformer-compatible form, ensuring that precise numerical formatting, distinct digit identity, and robustness to common normalization operations are maintained throughout the LLM pipeline. Experiments across five context-enriched forecasting benchmarks demonstrate that TempoWave consistently improves LLM-based forecasters over standard numeric tokenization and alternative embedding interfaces, achieving a new state-of-the-art. These results highlight the numeric interface as a key bottleneck and suggest that principled multi-resolution embeddings can better couple LLMs' contextual reasoning with precise forecasting. Our code is available at https://github.com/DC-research/TempoWAVE and our model can be accessed at https://huggingface.co/Melady/TempoWAVE.